# Any intuition for why eigenvector centrality relates to walks of infinite length?

Some centrality measures can be interpreted in terms of walks.

1. Degree centrality relates to a walk of length one: The more walks of length one reach a node, the higher this centrality measure.
2. Betweenness centrality relates to walks along the shortest paths. The higher the number of shortest paths that pass through a node, the higher this centrality measure.
3. Eigenvector centrality relates to a walk of infinite length according to the Wikipedia entry about centrality measures.

I find this characterization of these centrality measures quite useful but I have difficulties developing an intuition why eigenvector centrality relates to walk of infinite length. Any idea?